CE451 Midterm

CE451 Midterm - CE451 Water Resource Engineering...

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Unformatted text preview: CE451 Water Resource Engineering Midterm‐Term Examination March 10,2010 Professor Costas E. Synolakis 1. The hydrograph shown below is a unit hydrograph for a one hour rainstorm. a) Determine the area of watershed in acres b) A 3hr rain storm resulted in a runoff of 5 inches, what would be the resulting hydrograph for the 5 inch runoff? Note: 1 acre=43,560 ft2 4500 4000 3500 3000 2500 Q (cfs) 2000 1500 1000 500 0 0 0 1 2 T (hour) 3 4 0 5 1500 3000 4000 2. A well 12 inch in diameter penetrates 120 ft bellow static water table. After a certain period of time in pumping at rate of 300 gpm, the drawdown in the wells located at 60 ft and 140 ft from the pumping well are found to be 12 ft and 8 ft respectively, compute the followings: a) What is hydraulic conductivity in ft/day? b) What is Transimisivity coefficient in ft2/day? c) What is the approximate drawdown in pumping well? 1 ft3=7.48 gallons 3. Assume that the probability density function follows Lognormal distribution. The frequency analysis of a river gives the following results: 5yr. recurrence interval, peak flow at 10,000 cfs 50 yr. recurrence interval, peak flow at 60,000 cfs a) What peak flow will have return period of 100 year? b) What is a probability that a flow of 40,000 cfs or greater will not occur in next 10 years? c) During a construction of the dam, a diversion tunnel is to be used. Find the design flow for this tunnel such that we have a 15% probability of surcharge above the top of the tunnel entrance during a 16 months construction period. 4. A gutter is designed to drain the water in a playground adjacent to a parking lot. The dimensions are given as shown. The gutter speed designed to be 2.5 ft per second. The rainfall intensity is found to follow the negative exponential equation as given. The lateral flow time is assumed to be five minute for parking lot and 30 minutes for playground. The runoff coefficient for the parking lot is 0.9 and for playground is 0.3. Compute the design flow rate Q at the outlet of this composite area under various times of concentration (choose at least 3 times of concentration). i 3.0e 0.03t where i is rainfall intensity in in/hr and t is in minutes 800 ft 200 ft Q 600 ft Parking lot K=0.9 Playground K=0.3 5 min 20 min 5. Write one page on why we study water Resource Engineering and provide a couple of BIG picture examples that you will be able to address upon completion of the class. 1)Answer N 1 V Qi [(0 4000) (4000 3000) (3000 1500) (1500 0)]*1*60*60 30, 600, 000 ft 3 2 I 1 30600000 Area of watershed A 367200000 ft 2 1 12 367200000 A 8430 acres 43560 16000 14000 12000 10000 Q (cfs) 8000 6000 4000 2000 0 0 0 0.0 1 2 3 T (hour) 4 6666.7 4000 3000 1500 0 5 6 7500.0 11666.7 14166.7 2500.0 0.0 7 T(hr) 0 1 2 3 4 5 6 Q(cfs) 0 4000 3000 1500 0 Q1=Q*5/3 0.0 6666.7 5000.0 2500.0 0.0 Q1=Q*5/3 0.0 0.0 6666.7 5000.0 2500.0 0.0 Q1=Q*5/3 0.0 0.0 0.0 6666.7 5000.0 2500.0 0.0 Total Q(cfs) 0.0 6666.7 11666.7 14166.7 7500.0 2500.0 0.0 2) Answer Q 300* 24*60 / 7.48 57, 754 ft 3 / day h1 120 12 108 ft h2 120 8 112 ft r1 60 ft r2 140 ft r 140 Q ln( 2 ) 57754 ln( ) r1 K (h h ) 60 48935 17.7 ft / day Q K r2 (h22 h12 ) (1122 1082 ) 2764.6 ln( ) r1 2 2 2 1 T K 2 hwell h1 h2 108 112 17.7 1947 ft 2 / day 2 2 r 57754 0.5 Q 2 ln( well ) hwell 1082 ln( ) 6691.6 hwell 81.8 ft h12 K *17.7 60 r1 zwell 120 81.8 38 ft 3) Answer a) 74,000 cfs b) From graph T=20yr,p=1/20=0.05, Probability that it will not happen within next 10 years= (1‐0.05)10=0.599=59% C) J=0.15=1‐(1‐P) 16/12 P=0.1148 , T=1/0.1148,=8.7 years, Q=22,000 cfs 4) Answer: Q K PLiAPL K PG iAPG 2.5 ft / s 2.5*60 150 ft / min 800 /150 5.3 min start with t c 5.3min i 3.0e 0.03t 2.6 in / hr 0.22 ft / hr APL (0.3*150 800) * 200 / 2 84500 ft 2 APG (0.3* 20 0) *800 / 2 2400 ft 2 Q 0.9*0.22*84500 0.3*0.22* 2400 16889 ft 3 / hr Assume t c 11.3min i 3.0e 0.03t 2.137in / hr 0.178 ft / hr APL 200*800 160000 ft 2 APG (5* 20 11.3* 20) *800 / 2 130400 ft 2 Q 0.9*0.178*160000 0.3*0.178*130400 32595 ft 3 / hr ...
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